On a surface offering turn for the spinners and trouble for batsmen, the hosts raised hope of a series-levelling victory by reaching 268 for seven at the break, having resumed on 152-3.
Shuvagata Hom was unbeaten on 15, with Sabbir Rahman's dismissal to Adil Rashid sending the players in for lunch.
Imrul Kayes, unbeaten overnight, and Shakib Al Hasan added 48 for the fourth wicket during a chance-filled partnership.
Kayes was dropped twice before off-spinner Moeen Ali finally trapped him leg before for 78.
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Wicketkeeper Jonny Bairstow missed a stumping chance with Shakib on 16 before Ben Duckett grassed a simple catch in the deep with the batsman on 23.
England also missed two review opportunities with replays showing the umpire's decisions would have been overturned and Shakib continued to frustrate the tourists with a stroke-filled innings of 41 featuring six fours.
Bangladesh lost Shakib and captain Mushfiqur Rahim on the same score, with leg-spinner Rashid breaking the fifth-wicket stand in his first over of the day.
All-rounder Ben Stokes has troubled Mushfiqur (nine) throughout the test series and had the right-hander edge to Alastair Cook after the Pakistan captain was dropped on six.
Sabbir and Hom continued to attack the bowlers in a brisk stand of 30. A few heated words were exchanged between players from both sides during the partnership, prompting the umpires to intervene.
Rashid ended the stand with a straight delivery trapping Sabbir leg before for 15.
(Reporting by Sudipto Ganguly in Mumbai; Editing by Ian Ransom)
